Calculating Charge in a Concentric Spherical Region

[Pruddy]

1. Homework Statement

-38.0 nC of charge is uniformly distributed throughout a spherical volume of radius 34.0 cm.
How much charge is contained in a region of radius 23.0 cm concentric with the charge distribution?

Homework Equations

Charge density = λ/area

The Attempt at a Solution

I don't know how to approach this problem. I don't know if it is right to use gaus's law.Please if anyone can give me directions or what topic in physics this problem comes from, I will gladly appreciate. Thanks

 

[tiny-tim]

Hi Pruddy!

-38.0 nC of charge is uniformly distributed throughout a spherical volume of radius 34.0 cm.
How much charge is contained in a region of radius 23.0 cm concentric with the charge distribution?

You're told that the distribution is uniform, so this is just geometry …

"-38.0 kg of cheese is uniformly distributed throughout a spherical volume of radius 34.0 cm.
How much cheese is contained in a region of radius 23.0 cm concentric with the cheese distribution?" ​

 

[Pruddy]

Tiny-Tim,
So am I to used the Electric flux formula to solve this problem? But the question is looking for how much charge?

 

[ap123]

This question has nothing to do with the Gauss's Law or electric flux ( since it doesn't mention the electric field ).

As pointed out in post #2, this is a geometry problem.

Imagine starting with your sphere and removing a section with radius 23cm.
What is the relation between the removed part and the whole sphere?

 

[Doc Al]

Charge density = λ/area

What you need is charge density ρ = Q/volume.

How does the total volume (radius 34 cm) compare to the volume of the region (radius 23 cm)?

 

[whynot314]

Set up a Ratio, \frac{-38nc}{V_{1}}=\frac{Q_{2}}{V_{2}}

 

[Pruddy]

Hi, whynot314.
I used the formula and this are my calculations:

q2 = -38 x 10^(-9)/4*pi*r(0.34)^2 = q2/(4*pi*r(0.23)^2

= -38 x 10^(-9)*4*pi*r(0.23)^2 /(4*pi*r(0.34)^2
= -2.293 x 10^(-9)
I don't know if this is right...

 

[Dick]

Hi, whynot314.
I used the formula and this are my calculations:

q2 = -38 x 10^(-9)/4*pi*r(0.34)^2 = q2/(4*pi*r(0.23)^2

= -38 x 10^(-9)*4*pi*r(0.23)^2 /(4*pi*r(0.34)^2
= -2.293 x 10^(-9)
I don't know if this is right...

You should be using volumes, not surface areas. This isn't a Gauss' law problem. It's a charge density problem. The volume of a sphere of radius r is (4/3)pi*r^3. But even using area the numbers still don't come out the way you say they do.

 

[Pruddy]

Hi, whynot314,
Thanks a lot! You are the best.

 

[Pruddy]

Hi, whynot314,
I got it now.

 

[whynot314]

I am studying this stuff right now to so this problem helped me as well.

 

[Pruddy]

wow. That's awesome!